George Osborne's budget last week reaffirmed the government line that there is no alternative to immediate austerity. On the streets of London yesterday, hundreds of thousands of citizens disagreed.

Even in the most straitened circumstances, there is always a range of options: who is taxed, who is spared, which departments' budgets are protected, which are not. In that sense, the marchers have self-evident truth on their side. Public service cuts express political choices, not immutable forces of nature.

But there is also an important truth in Mr Osborne's position. Last year, when the coalition was formed, the UK had a budget deficit of around 12% of GDP; the government was being forced to borrow some £140bn just to cover the annual overspend on public services.

There are multiple explanations for that state of affairs. Reckless profligacy by Gordon Brown, say Tories; emergency measures to cushion the country from a global crisis, say Labour. But there is no serious dispute about the need to bring the deficit down, only about the best timetable. Labour leader Ed Miliband's principal line of attack is that the government is going "too far, too fast". And yet, going slower would still hurt. There are choices aplenty, but none is easy.

The government is determined to eliminate the deficit within four years, regardless of any variations in the economic climate. There is no Plan B.

So, under the strictures of Plan A, Mr Osborne's budget last week had to be "fiscally neutral", meaning that every pound given away was clawed back elsewhere. There were some of the usual populist manoeuvres – some pennies off petrol made easy headlines. And there were a couple of meaty reforms – raising the personal tax allowance; cutting corporation tax.

But in terms of the bigger picture, every Treasury calculation flows from a bet the chancellor made last year on a sudden private sector renaissance paying off. The idea is that a macho display of fiscal discipline, combined with some tax incentives and deregulation, will give businesses confidence in the long-term stability of the UK economy, thereby prompting them to invest.

The danger is that austerity drives up unemployment and hits people's spending power before the recovery has a chance to gather pace. The government then ends up spending more on benefits and taking less in taxes, which undermines the original goal of reducing the deficit.

This theoretical economic argument over the wisdom of cutting has reached an impasse. Only developments in the real economy will prove one side right. Meanwhile, the cuts themselves are on the way to becoming a political fait accompli. Many people will continue to demand that spending on public services should be protected – yesterday's demonstration will not be the last. But with no sign that the government is wavering, debate in policy terms will soon have to move on to the broader question of what the public sector should look like in austere times.

That poses a challenge to the anti-cuts movement. Yesterday's march proved that the relationship between the British people and their public services is about more than value-for-money transactions. The fact that so many people turned out indicates an emotional involvement, one that recognises how government-funded institutions can be part of the social fabric. Contrary to David Cameron's belief that the two are antithetical, society and the state sometimes happily merge.

But a mass show of affection does not bring the opposition any closer to a sustainable funding model for public services. There is a tendency among trade unions and sections of the Labour party to present the cuts as an exclusively ideological assault on the welfare state. Among some Conservatives, it is. But there remains the awkward, non-ideological fact that government revenues in 2011 will not cover the cost of services as they were provided in 2007, at the top of the boom.

There will be plenty of opportunities in the months ahead to denounce individual strokes of the Treasury axe. But the big question at the centre of British politics is not: "Do we want good services?" Plainly we do. It is: "How will we pay for them?"

The cuts are only half of the government's programme. The coalition is proposing radical restructuring of the NHS, epic upheaval in the way schools are run, the biggest changes to welfare since the Second World War, a "revolution" in penal policy, major changes to policing and an overhaul of the state pension, alongside many smaller-scale initiatives.

Some of these projects are ideologically motivated; some are pragmatic responses to funding shortfalls; some seem driven as much by personal ministerial ambition as public policy rationale. But the overall political impression is of a high-octane administration roaring off down the road, leaving the opposition spluttering in the dust. That is the product of a deliberate – and, so far, effective – strategy by the coalition to make irreversible changes before the opposition has had a chance to organise its response.

Labour is being pushed into a stance of perpetual carping. Their answer to the question of public sector reform by the time of the next election risks amounting to little more than: "Well, we wouldn't start from here."

Ed Miliband is right to tap into anxiety that deficit reduction is happening too fast. But that view contains the tacit recognition that it must still happen at some stage. Any credible alternative to the cuts must include some ideas about the long-term financial sustainability of the welfare state. That will be true even if Labour are proved right about the macro-economic folly of extreme austerity. "We told you so," is also not a very appealing campaign slogan.

In other words, it should be possible to argue against the economic gambles taken by Mr Osborne and also accept the need for a radical approach to delivering public services when the Exchequer is cash-starved. The coalition has a clear programme. There is much to dislike in it, and good reasons for the public to mistrust aspects of it. But there are also bound to be some ideas worth embracing and many that invite constructive dialogue.

Over the next few years, political debate should be about competing visions of the economy, society and the state's role in both. At the moment, on the vital matter of public sector reform, the coalition agenda is pretty much the only game in town. A crowd hundreds of thousands strong yesterday demanded an alternative. That would be a truly formidable force in politics, if only someone could express what the alternative is.